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Consider real numbers $x_1, \dots, x_M$ such that

$$\sum_{i=1}^{M} \frac{\cos(x_i t^2)}{e^{(x_it)^2}} \le -\frac{1}{2}, $$

for all $L< t <L^A,$ where L is a large number.

What lower bound we can get for M?

I think its not hard to get something like M>A but I expect much larger lower bound.

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